A cautionary note on Bayesian estimation of population size by removal sampling with diffuse priors.

Area of Science:

• Ecology
• Statistics
• Population Dynamics

Background:

• Removal sampling is a common ecological method for estimating population size.
• Bayesian inference is widely used but can be sensitive to prior specification, especially with unknown sampling rates.

Purpose of the Study:

• To investigate the impact of prior choices on Bayesian population size estimation using removal sampling.
• To identify methods for stabilizing estimates when the sampling rate is unknown.

Main Methods:

• Analysis of the likelihood function in removal sampling models.
• Evaluation of Bayesian estimators using default improper and weakly informative priors.
• Theoretical derivations and simulation studies to assess estimator performance.
• Application of findings to real-world ecological datasets.

Main Results:

• Default improper priors can lead to improper posteriors or infinite population size estimates.
• Weakly informative priors result in unstable estimators sensitive to hyperparameter choices.
• Penalizing small sampling rates or large population sizes stabilizes estimates.
• Recommendations for prior selection are provided based on theoretical and simulation results.

Conclusions:

• Careful prior selection is crucial for robust Bayesian population size estimation in removal sampling.
• The study offers practical guidance for ecologists and statisticians using these methods.
• Stabilized estimation strategies improve the reliability of population size assessments.